EP1309849A2 - Procede d'interpolation de bases de donnees destine a la mesure optique de microstructures a diffraction - Google Patents

Procede d'interpolation de bases de donnees destine a la mesure optique de microstructures a diffraction

Info

Publication number
EP1309849A2
EP1309849A2 EP01957510A EP01957510A EP1309849A2 EP 1309849 A2 EP1309849 A2 EP 1309849A2 EP 01957510 A EP01957510 A EP 01957510A EP 01957510 A EP01957510 A EP 01957510A EP 1309849 A2 EP1309849 A2 EP 1309849A2
Authority
EP
European Patent Office
Prior art keywords
inteφolation
sample
measurement
optical
parameters
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Withdrawn
Application number
EP01957510A
Other languages
German (de)
English (en)
Inventor
Kenneth C. Johnson
Fred E. Stanke
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Therma Wave Inc
Original Assignee
Therma Wave Inc
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Therma Wave Inc filed Critical Therma Wave Inc
Publication of EP1309849A2 publication Critical patent/EP1309849A2/fr
Withdrawn legal-status Critical Current

Links

Classifications

    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B5/00—Optical elements other than lenses
    • G02B5/18—Diffraction gratings
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
    • G01N21/47—Scattering, i.e. diffuse reflection
    • G01N21/4788—Diffraction
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/84—Systems specially adapted for particular applications
    • G01N21/88—Investigating the presence of flaws or contamination
    • G01N21/95—Investigating the presence of flaws or contamination characterised by the material or shape of the object to be examined
    • G01N21/9501—Semiconductor wafers
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/84—Systems specially adapted for particular applications
    • G01N21/88—Investigating the presence of flaws or contamination
    • G01N21/95—Investigating the presence of flaws or contamination characterised by the material or shape of the object to be examined
    • G01N21/956—Inspecting patterns on the surface of objects

Definitions

  • the present invention relates to optical measurement of parameters of interest on samples having diffractive structures thereon, and in particular relates to improvements in real-time analysis of the measured optical signal characteristics from a sample to determine parameter values for that sample.
  • Optical measurement methods are typically used for high-speed, non-destructive measurement of such structures. With such methods, a small area on a measurement sample is illuminated with optical radiation comprising one or more wavelengths, and the sample properties over the illuminated area are determined by measuring characteristics of radiation reflected or diffracted by the sample (e.g., reflection intensity, polarization state, or angular distribution).
  • This disclosure relates to the measurement of a sample comprising a diffractive structure formed on or in a substrate, wherein lateral material inhomogeneities in the structure give rise to optical diffraction effects. If the lateral inhomogeneities are periodic with a period significantly smaller than the illuminating wavelengths, then diffracted orders other than the zeroth order may all be evanescent and not directly observable, or may be scattered outside the detection instrument's field of view. But the lateral structure geometry can nevertheless significantly affect the zeroth-order reflectivity, making it possible to measure structure features much smaller than the illuminating wavelengths.
  • the components of the characteristic might, for example, represent reflectivities at different wavelengths or collection angles.
  • the measurement process comprises the following steps: First, a set of trial values of the measurement parameters is selected. Then, based on these values a computer- representable model of the measurement sample structure (including its optical materials and geometry) is constructed. The electromagnetic interaction between the sample structure and illuminating radiation is numerically simulated to calculate a predicted optical signal characteristic, which is compared to the measured signal characteristic. An automated fitting optimization algorithm iteratively adjusts the trial parameter values and repeats the above process to minimize the discrepancy between the measured and predicted signal characteristic. (The optimization algorithm might typically minimize the mean-square error of the signal characteristic components.)
  • ILS Inverse Least Squares
  • PCR Principal Component Regression
  • PLS Partial Least Squares
  • the linear coefficients of the approximate model are determined by a multivariate statistical analysis technique that minimizes the mean-square error between exact and approximate data points in a "calibration" data set.
  • the calibration data may be generated either from empirical measurements or from exact theoretical modeling simulations. This is done prior to measurement, so the calibration process does not impact measurement time.
  • the various linear models (ILS, PCR, PLS) differ in the type of statistical analysis method employed.
  • the linear approximation can only be applied over a limited range of measurement parameter values; and second, within this range the approximate model does not generally provide an exact fit to the calibration data points. (If the calibration data is empirically determined, one may not want the model to exactly fit the data, because the data could be corrupted by experimental noise. But if the data is determined from a theoretical model it would be preferable to use an approximation model that at least fits the calibration data points.) These deficiencies can be partially remedied by using a non-linear (e.g., quadratic) functional approximation (Ref. 7). This approach mitigates, but does not eliminate, the limitations of linear models.
  • a non-linear (e.g., quadratic) functional approximation Ref. 7
  • the parameter range limit of functional (linear or non-linear) approximation models can be extended by the method of "range splitting", wherein the full parameter range is split into a number of subranges, and a different approximate model is used for each subrange (Ref. 7).
  • the method is illustrated conceptually in Fig. 1 (cf. Fig. 2 in Ref. 7), which represents the relationship between a measurement parameter x, such as a linewidth parameter, and an optical signal characteristic y, such as the zeroth- order sample reflectivity at a particular collection angle and wavelength.
  • a measurement parameter x such as a linewidth parameter
  • an optical signal characteristic y such as the zeroth- order sample reflectivity at a particular collection angle and wavelength.
  • a set of calibration data points (e.g., point 101) is generated, either empirically or by theoretical modeling.
  • the x parameter range is split into two (or more) subranges 102 and 103, and the set of calibration points is separated into corresponding subsets 104 and 105, depending on which subrange each point is in.
  • a statistical analysis technique is applied to each subset to generate a separate approximation model (e.g., a linear model) for each subrange, such as linear model 106 for subrange 102 and model
  • the range-splitting method has additional deficiencies.
  • the functional approximation is continuous and smooth within each subrange, it may exhibit discontinuities between subranges (such as discontinuity 108 in Fig. 1). These discontinuities can create numerical instabilities in optimization algorithms that estimate measurement parameters from optical signal data. The discontinuities can also be problematic for process monitoring and control because small changes in process conditions could result in large, discontinuous jumps in measurements.
  • Another drawback of the range-splitting model is the large number of required calibration points and the large amount of data that must be stored in the model. In the Fig. 1 illustration, each subrange uses a simple linear approximation model of the form
  • a and b are calibration coefficients. At least two calibration points per subrange are required to determine a and b (generally, more than two are used to provide good statistical sampling over each subrange), and two coefficients (a and b) must be stored for each subrange. If there are M subranges the total number of calibration points must be at least 2 M, and the number of calibration coefficients is 2 M. Considering a more general situation in which there are N measurement parameters x l5 x 2 , ... x N , the linear approximation would take the form
  • Fig. 2 illustrates a parameter space spanned by two parameters, x ⁇ and x 2 .
  • the Xi range is split into three subranges 201, 202, and 203, and the x 2 subrange is split into three subranges 204, 205, and 206.
  • the optical signal characteristic (y) comprises multiple signal components (e.g., for different wavelengths)
  • the number of calibration coefficients will increase in proportion to the number of components.
  • a nonlinear (e.g., quadratic) subrange model is used, the number of calibration points and coefficients would be vastly larger.
  • Another measurement approach Minimum Mean Square Error analysis
  • MMSE Ref s 2-9, 11, 13, 15
  • MMSE Ref s 2-9, 11, 13, 15
  • a database of pre-computed theoretical optical signal characteristics representing a large variety of measurement structures is searched and compared to a samples' measured optical signal, and the best-fitting comparison (in terms of a mean-square-error fitting criterion) determines the measurement result.
  • the above-noted references relate primarily to scatterometry and spectroscopy, but MMSE-type techniques have also been applied in the context of ellipsometry; see Ref s. 12 and 16.
  • the MMSE method is capable of modeling strong nonlinearities in the optical signal.
  • the invention is a method for measuring parameters of interest of a sample comprising a diffractive structure, wherein the method employs a database-search technique in combination with interpolation to avoid the tradeoff between measurement resolution and accuracy.
  • a theoretical model is provided, from which a theoretical optical response characteristic of the diffractive structure is calculable as a function of a set of one or more "interpolation parameters" corresponding to measurement parameters.
  • the theoretical model comprises two primary components: a method for translating any trial set of interpolation parameter values into a computer-representable model of the diffractive structure (including its optical materials and geometry), and a method for numerically simulating electromagnetic interactions within the diffractive structure to calculate the theoretical response characteristic.
  • a database of "interpolation points" and corresponding optical response characteristics is generated. Each interpolation point is defined by a specific interpolation parameter set consisting of specific values of the interpolation parameters.
  • the theoretical model is applied to each interpolation point to calculate its corresponding theoretical optical response characteristic, which is stored in the database.
  • the database is used by an "interpolation model", which calculates an interpolated optical response characteristic as a function of the interpolation parameter set.
  • the interpolation model provides an approximation to the theoretical model, but without the computational overhead. Given any trial interpolation parameter set within a defined parameter domain, the interpolation model computes an approximate corresponding optical response characteristic by interpolating (or perhaps extrapolating) on the database.
  • the parameter domain is typically limited by the database, although extrapolation can sometimes be used to extend the domain outside of the database limits.
  • the term "interpolation” can be broadly construed herein to include extrapolation.)
  • the diffractive structure's internal geometry need not be modeled, and electromagnetic interactions within the structure need not be simulated, in the interpolation model.
  • the interpolation model represents a substantially continuous function mapping the interpolation parameter set to the optical response characteristic - it does not exhibit the discontinuities or discretization of prior-art methods such as range-splitting and MMSE. Furthermore, although the interpolation is an approximation, the interpolated optical response characteristic accurately matches the theoretical optical response characteristic at the interpolation points represented in the database. Thus it does not suffer the accuracy limitation of prior-art functional approximation methods.
  • the term "interpolation” broadly connotes a fitting function that fits the interpolation points. A portion of the fitting function might actually be extrapolated, so in this context the distinction between "interpolation” and "extrapolation” is not significant.
  • the interpolation model is used by a fitting optimization algorithm that determines measurement parameters of a sample based on a measured optical signal characteristic of the sample.
  • the theoretical optical response characteristic which is approximated by the interpolation model, does not necessarily correspond directly to the optical signal characteristic or to a measurable quantity.
  • a predicted optical signal characteristic is calculable from the optical response characteristic by means of a computationally efficient algorithm that, like interpolation, does not require that the diffractive structure's internal geometry be modeled or that electromagnetic interactions within the structure be simulated.
  • the optimization algorithm automatically selects a succession of trial interpolation parameter sets, applies the interpolation model to calculate corresponding interpolated optical response characteristics, and from these calculates corresponding predicted optical signal characteristics, which are compared to the measured optical signal characteristic.
  • the algorithm selects the trial parameter sets, based on a comparison error minimization method, to iteratively reduce a defined comparison error metric until a defined termination criterion is satisfied.
  • the measured optical signal characteristic is acquired with a measurement instrument comprising an optical sensor system, which detects radiation diffracted from the sample.
  • the instrument further comprises computational hardware that applies the fitting optimization algorithm to measured signal data and generates measurement results. Subsequent to results generation, the instrument may also generate a computational or graphical representation of the diffractive structure's geometry. However, this representation is not necessarily required to calculate a corresponding predicted optical response or signal characteristic, and it need not correspond to a particular parameter set in the database.
  • Fig. 1 illustrates the "range-splitting" method of the prior art.
  • Fig. 2 illustrates a two-dimensional parameter space.
  • Fig. 3A illustrates a measurement sample comprising a diffractive, line-space grating structure.
  • Fig. 3B illustrates a diffractive structure comprising a two-dimensional array of holes.
  • Fig. 4 illustrates a plan view of a sample comprising two reflecting zones.
  • Fig. 5 A illustrates a measurement sample comprising a layered structure with one diffractive layer.
  • Fig. 5B illustrates a measurement sample comprising a layered structure with two diffractive layers.
  • Fig. 6A illustrates a plot of a measurement sample's complex reflection coefficient r as a function of a measurement parameter, x.
  • Fig. 6B illustrates the reflectivity signal
  • R r 2 corresponding to the reflection coefficient of Fig. 6A
  • Fig. 7 illustrates piecewise-linear interpolation on an optical response characteristic.
  • Fig. 8 illustrates the selection of trial parameter sets for refinement in the fitting optimization algorithm.
  • the measurement instrument :
  • the measurement instrument comprises a radiation source, illumination optics for conveying the radiation to a measurement sample, collection optics for conveying radiation reflected or diffracted from the sample to an optical sensor system, and computational hardware that controls the instrument and translates optical signal data from the sensor system into measurement results.
  • the instrument collects signal data as a function of one or more control variables such as wavelength, illumination and collection directions (each direction being characterized by polar and azimuthal angles relative to the sample), illumination polarization state, and the collection optics' polarization characteristics.
  • An instrument may scan a control variable or may have multiple sensor channels that simultaneously sample multiple values of the variable.
  • the illumination wavelength may be scanned, or the system may use broadband illumination in conjunction with a spectrometer detector to simultaneously sense multiple wavelength signals.
  • each sensor channel responds to radiation comprising a non-zero range of wavelengths, angles, and polarization states, and the fitting optimization algorithm may need to take this into account to obtain a good fit between predicted and measured signal characteristics.
  • the measurement sample :
  • the measurement sample is a periodic, line-space grating structure whose geometry is invariant with respect to translation in a particular direction.
  • Fig. 3 A illustrates a line-space structure comprising grating lines formed on a flat substrate.
  • the structure is translationally invariant in the Z direction, and it has a preiodicity dimension A in the X direction.
  • the structure geometry is fully characterized by its two-dimensional cross-section in an X-Y plane.
  • Fig. 3B illustrates another type of measurement sample comprising a two- dimensional array of holes in a substrate.
  • the geometry can be described in terms of a
  • grating cell which is repeated periodically in the X-Z plane, and is characterized in terms of two fundamental periods, ⁇ i and ⁇ 2 .
  • Periodic structures such as those illustrated in Fig's. 3 A and 3B have the property that, when illuminated by a narrow beam of radiation, the back-scattered radiation comprises a discrete set of narrow beams, or "diffracted orders". These orders include the specularaly reflected ("zeroth order") component of the scattered radiation. Generally, structures with smaller periods produce fewer orders, and if the periodicity is sufficiently fine no orders other than the zeroth order will propagate from the structure.
  • the measurement instrument may be configured to selectively exclude, or accept, a particular diffracted order or orders. In typical applications, only the zeroth order is used.
  • Fig. 4 illustrates a plan view of a sample comprising two reflecting zones, a first zone 401 comprising a diffractive line- space structure, and a second adjacent zone 402 that is laterally homogeneous.
  • the illuminating radiation covers a measurement spot 403 that straddles both zones.
  • the measurement sample is typically a layered structure, such as that illustrated cross-sectionally in Fig. 5 A or 5B.
  • Fig. 5 A illustrates a sample comprising a diffractive structure 501 sandwiched between a non-diffractive substructure 501 and a non-diffractive superstructure 503.
  • the non-diffractive structures may each comprise multiple layers, which may be homogeneous or may have refractive index gradients, but which are typically laterally homogeneous (i.e., the refractive index only varies in the direction normal to the substrate).
  • Fig. 5B illustrates a sample type in which the substructure 502 contains a second diffractive layer. Depending on how the method of the invention is applied, the subject
  • diffractive structure of the method may be interpreted as the sample as a whole (or more specifically, a portion of the sample in the vicinity of the measurement spot), or as a component of the sample.
  • the subject diffractive structure could be the diffractive zone 401 in Fig. 4, or the diffractive layer 501 in Fig. 5 A or 5B.
  • a model of the diffractive structure including its optical materials and geometry
  • a model of the electromagnetic interactions within the diffractive sample which determine the sample's diffractive optical properties.
  • the subject theoretical model of the invention method does not necessarily characterize the sample as a whole - it characterizes the subject diffractive structure, which may only be one of a number of components of the sample; and the subject theoretical model may itself be a component of a broader theoretical model that characterizes the whole sample.
  • the measurement sample structure is typically represented computationally as a function of one or more "sample parameters” (e.g., linewidth, layer thicknesses, material parameters), some of which are known in advance and some of which are determined by measurement. Of the latter “measurement parameters”, some or all are associated with the subject diffractive structure - these are termed “interpolation parameters” herein.
  • sample parameters e.g., linewidth, layer thicknesses, material parameters
  • the theoretical model Given any particular interpolation parameter set, the theoretical model generates a computational representation of the diffractive structure; it performs a numerical simulation of electromagnetic propagation of radiation through the interior of the diffractive structure; and based on the electromagnetic simulation it calculates a theoretical optical response characteristic of the diffractive structure.
  • This response characteristic may, in some applications, need to be combined with optical response characteristics of other components of the sample (e.g. the non-diffractive structure 402 of Fig. 4 or the substructure 502 or super structure 503 of Fig. 5A or 5B) to characterize the whole sample.
  • This combining process may include modeling electromagnetic interactions at the interfaces between the components (i.e., applying boundary conditions).
  • the processes of generating the other components' response characteristics and combining them with the subject diffractive structure's response characteristic do not require that the diffractive structure's internal geometry (e.g. profile shape) be modeled or that the electromagnetic propagation within the diffractive structure be simulated.
  • the optical response characteristic could comprise a measurable quantity such as reflectivity.
  • the response characteristic comprises complex reflectance coefficients (or generalizations of the complex reflectance coefficient, which will be discussed below), which are not directly measurable.
  • the measurable reflectivity is a real-valued quantity that is calculable from the complex reflectance coefficient.
  • the "signal characteristic” is a measurable quantity that can be obtained from, or is calculable from, a signal generated by the measurement instrument's optical sensor system.
  • the signal characteristic depends on the instrument's optical characteristics, as well as the sample. For example, the polarization characteristics of the illuminating radiation or of the collection optics may need to be taken into account in calculating the predicted signal.
  • the instrument's optical characteristics, such as polarization may be controlled during data acquisition, and may be represented by instrument calibration quantities that can vary from instrument to instrument.
  • the measurable signal characteristic depends on the entire sample structure and the instrument characteristics - it cannot generally be separated into components associated with individual sample components or with the instrument, whereas such a separation can often be performed with complex reflectance-type quantities. (Reflecting samples that exhibit significant polarizing properties can be characterized in terms of a "reflectance Jones matrix", which is a generalization of the complex reflectance coefficient. See Section 27.7 in Ref. 17 for a description of the Jones matrix.)
  • the A, B, and C terms in this expression are "mixing coefficients" which may be sample parameters or functions of sample parameters. (They may also be functions of the instrument's optical properties.)
  • the r terms are the optical response characteristics of the reflecting zones.
  • the mixing model calculates R, an "effective reflectivity", which corresponds to a measurable signal characteristic of the sample.
  • Fig. 4 illustrates a two-zone sample comprising a diffracting zone 401 and a non-diffracting zone 402.
  • the subject theoretical model of the present invention calculates r ⁇ as a function of interpolation parameters.
  • This theoretical model is a component of a broader theoretical model - the mixing model - that computes the sample's signal characteristic R by combining ri with the optical response characteristics of the other adjoining zone or zones, in accordance with Eq. 3.
  • Multi-layer structures such as those illustrated in Fig's. 5A and 5B can be similarly partitioned into separate components (layers, in this case), each represented by its own optical response characteristic.
  • Theoretical models for these types of structures typically represent the illumination and diffracted radiation as plane-wave expansions.
  • a plane wave is a simplifying mathematical abstraction that is infinite in spatial and temporal extent. Each plane wave has a specific direction of propagation, wavelength, and polarization state. When a periodic structure is illuminated with a plane wave, it scatters the illumination into a discrete set of plane waves, or
  • diffracted orders which may include both transmitted and reflected orders.
  • the undeviated transmitted order is termed the "zeroth transmitted order”
  • specularly reflected reflected order is termed the "zeroth reflected order”.
  • the ratios of the diffracted orders' complex amplitudes to the incident plane wave's complex amplitude are termed "complex scattering coefficients”.
  • complex scattering coefficients These include reflectance scattering coefficients for reflected orders and transmittance scattering coefficients for transmitted orders).
  • Each order is characterized by two scalar scattering coefficients corresponding to two constituent polarization components of the order (e.g., orthogonal linear polarization components). Furthermore, each of these coefficients depends on the polarization state of the incident illumination, so considering two independent incident polarization states, each order will actually have four associated scalar scattering coefficients corresponding to any particular wavelength and incidence direction.
  • a theoretical optical model of the sample will calculate the complex scattering coefficients of one or more diffracted orders as a function of the incident plane wave's direction, wavelength, and polarization state.
  • the aggregation of the individual complex scattering coefficients could constitute the structure's optical response characteristic.
  • the subject diffractive structure is an individual layer component in a layered structure, such as element 501 in Fig. 5 A or 5B
  • the optical response characteristic could comprise a "scattering matrix", which represents a linear relationship between complex amplitudes of electromagnetic field components at the diffractive layers two bounding surfaces, 504 and 505.
  • Other layers in the sample may be similarly represented by scattering matrices.
  • the multiple scattering matrices of the different layers may be combined to form a composite scattering matrix for the entire sample, from which the scattering coefficients are readily obtained.
  • S- matrices scattering matrices
  • Ref. 18 an algorithm for combining scattering matrices (S- matrices) of adjacent layers is described in Ref. 18 (see especially equation 15A).
  • S-matrix or R-matrix formulations described in this published article could be used to define a diffractive layer's optical response characteristic.
  • the process of combining the optical response characteristics is much simpler and quicker than the computation of the layers' response characteristics themselves (at least for diffractive layers), and could potentially be performed during a real-time measurement process.
  • the subject theoretical model of the invention could be a component of a hierarchy of theoretical optical models.
  • the subject theoretical model could calculate an optical response characteristic (e.g., an S-matrix) characterizing diffractive layer 501 in the multilayer structure of Fig. 5 A or 5B.
  • This model would be a component of a second-tier theoretical model that calculates an optical response characteristic for the entire multilayer structure.
  • This structure may represent just one of multiple reflecting zones, such as zone 401 in Fig. 4, and the structure's corresponding second-tier theoretical model may be a component of a third-tier theoretical model (e.g. a mixing model) that calculates a diffraction response characteristic for the entire multi-zone measurement sample.
  • a third-tier theoretical model e.g. a mixing model
  • the interpolation database The theoretical model is applied to each of a plurality of "interpolation points", each point defined by a specific interpolation parameter set consisting of specific values of the interpolation parameters. For each interpolation point, a corresponding optical response characteristic of the diffractive structure is calculated and stored in the database.
  • each stored optical response characteristic comprises a plurality of complex reflectance coefficients or scattering matrices associated with different illumination wavelengths, incidence directions, and polarization states, but all associated with the same diffractive structure configuration (materials and geometry).
  • the computational representation of the associated structure geometry e.g., profile shape) is not required for subsequent measurement processes and need not be stored in the database.
  • the interpolation model uses the database to estimate the optical response characteristic for interpolation parameter sets that are not necessarily represented in the database.
  • the interpolation model defines a continuous function relating any trial interpolation set to a corresponding optical response characteristic, and in a preferred embodiment the response function is also smooth (i.e., continuously differentiable).
  • the continuity and smoothness may be limited by practical limitations such as data discretization, but the function is "substantially continuous” in the sense that any actual discontinuities are insignificant in comparison to the data discretization in the database.
  • the interpolation function substantially matches the theoretical optical response characteristic at the database interpolation points, in the sense that any slight mismatch is insignificant from the perspective of measurement performance.
  • the interpolation function is defined over a parameter domain that typically covers the database interpolation points.
  • the parameter domain may possibly be extended by extrapolation.
  • the accuracy of extrapolation is usually very poor, but in some cases the functional dependence of the optical response characteristic on a particular interpolation parameter may be very nearly linear, in which case extrapolation may be reliably applied to that parameter.
  • the interpolation function will exhibit accuracy errors at interpolation parameter sets that do not correspond to interpolation points, but these errors can be mitigated by interpolating on an optical response characteristic, such as complex reflectance, that is related to the (complex-valued) electromagnetic field amplitudes, rather than a signal-related response characteristic.
  • an optical response characteristic such as complex reflectance
  • Figs. 6A and 6B illustrates a plot of a measurement sample's complex reflection coefficient r (for some particular wavelength, incidence direction, and polarization state) as a function of a measurement parameter, x (e.g., linewidth).
  • x e.g., linewidth
  • Li the vicinity of the zero crossing 605 the signal plot 603 is very nonlinear, resulting in a poor interpolation fit; whereas the interpolation fit on the complex reflection coefficient is very accurate near the zero crossing. (The accuracy of the signal interpolation could be improved by using a nonlinear interpolating function. But regardless of what interpolation method is used, the interpolation fit would generally be better when applied to complex reflection coefficient.)
  • interpolation is piecewise-linear interpolation, which is illustrated in Fig. 7.
  • a single, scalar-valued optical response characteristic y is interpolated over a single, scalar- valued measurement parameter
  • the parameter is sampled in the database at uniformly-spaced parameter values, ⁇ [0], ⁇ [l], - x x [M] (wherein M is the number of sampling intervals), and y is linearly interpolated between the database values.
  • the ⁇ x l , y ⁇ pairs represented in the database are the "interpolation points", two of which are indicated in the figure as 701 and 702.
  • the corresponding interpolated y value denoted Y , is calculated by the following procedure. First, assuming that X x is within the sampling range (xr[0] ⁇ X, ⁇ x ] ), find an interpolation interval containing X, ,
  • the optical response characteristic y may be a composite entity such as a vector or a matrix.
  • the components of y may, for example, correspond to different scattering matrix coefficients and different combinations of wavelength, incidence direction, and polarization.
  • Each component x t of x is sampled in the database at uniformly- spaced values x-[0] , x[l] , ... x t [M t ] (wherein M i is the number of sampling intervals for x. ).
  • the database parameter range comprises a multi-dimensional array of "sampling grid cells", each cell being bounded in each i-th dimension by two successive parameter values ,[ ,] and x i [j i + 1] .
  • the interpolation algorithm approximates y as a multilinear function of x in each grid cell.
  • X ⁇ X 1 , X 2 ,... X N ⁇
  • the corresponding interpolated y value, denoted Y is calculated by the following procedure. First, find a grid cell containing Z , .[; ⁇ ] ⁇ Z,. ⁇ x,.[; ⁇ +l] Eq. 10
  • C i [k, , k 2 , ... k N ] represents linear interpolation coefficients of y with respect to parameter values x l ,...x i , which are spatially sampled at the grid cell limits of parameter values ⁇ . +1 ,...x N .
  • C i [k 1 ,k 2 ,...k N ] is generated from C M [k, , k 2 , ... k N ] by applying the one- dimensional interpolation method to the i - th parameter dimension ( x. ),
  • the derivatives of the interpolated quantity Y with respect to X t can be easily calculated using the above formalism. As will be seen later, the derivative information can be used to significantly enhance the runtime performance of the fitting optimization algorithm.
  • Improved interpolation accuracy can be obtained by using a multi-cubic, rather than multilinear, interpolating function in each grid cell.
  • a hybrid approach may be used in which linear interpolation is used for some parameters, and cubic interpolation is used for others.
  • the one-dimensional cubic interpolation case can be illustrated with reference to Fig. 7.
  • the interpolated value Y is approximated as a cubic function of X, .
  • the coefficients of the cubic function are chosen so that the interpolation fits both the database y values and the finite-difference derivatives of y with respect to x, at the interpolation interval boundaries.
  • the derivative y f (x 1 [j]) at point -f ] is estimated as
  • the one-dimensional cubic interpolation algorithm proceeds as follows. First, Z x is assumed to be within an interior sampling interval, T ⁇ Z ⁇ T ⁇ + l] 1 ⁇ 7 ⁇ -1 Eq.16
  • a three-point quadratic fit may be applied in the boundary intervals.
  • the term y(x 1 [j -1]) in Eq. 23 is undefined (i.e., not in the database), so the C x [-1] term is omitted and the C 0] , C x [l] , and C, [2] terms are quadratic functions of t with quadratic coefficients selected so that the interpolated Y value matches the database when X, is equal to O] , x x [l] , or x, [2] .
  • This fit function is used in the interval x,[0] ⁇ X, ⁇ x l] .
  • the quadratic fit function can be extrapolated for values Z x ⁇ x 1 [0] .
  • U cubic interpolation is applied in the adjacent interval (x l] ⁇ Z j ⁇ X j [2]) the interpolated Y value will be both continuous and continuously differentiable (smooth) with respect to Z x at X t - [l] .
  • the interpolation coefficients ( C N [k t , k 2 , ...] ) are preferably not pre- computed, but generated in real time during the measurement process so that the interpolation relies only on optical response data stored in the database. Furthermore, derivatives of Y with respect to Z can also be computed in real time. The interpolation method does not require that any extraneous data such as interpolation coefficients or derivatives be stored in the database.
  • interpolation methods for example linear or quadratic interpolation on a triangular or simplex-shaped sampling grid, or multi-dimensional spline interpolation, could also be used.
  • the above methods may appear to be constraining, in that parameters are all sampled at uniform intervals over a rectangular region of parameter space.
  • the algorithm designer has a great degree of freedom in how the interpolation parameters are defined, which largely offsets this limitation.
  • the linewidth can be represented as a nonlinear function of a uniformly-sampled interpolation parameter, with the functional mapping chosen so that small linewidths are sampled more finely than large linewidths.
  • the primary distinguishing features of the interpolation method are that it defines a substantially continuous function of interpolation parameters over a parameter domain that includes the interpolation points, and the interpolated optical response characteristic substantially matches the theoretical optical response characteristic at the interpolation points.
  • the fitting optimization algorithm iteratively compares the measured optical signal characteristic of the measurement sample with a plurality of predicted optical signal characteristics determined from corresponding interpolated optical response characteristics to find a best-fit parameter set, which defines the measured parameters of the sample.
  • the predicted optical signal characteristic is determined from the interpolated optical response characteristic, which is obtained from the interpolation model.
  • the optical response characteristic is a quantity or composition of quantities such as complex reflectance coefficients from which the signal characteristic is calculated in real time (i.e. after acquiring the measured signal). This calculation involves several steps. First, if the optical response characteristic represented in the interpolation database only characterizes a component of the sample (such as diffractive reflecting zone 401 in Fig. 4 or the diffractive layer 501 in Fig.
  • the interpolated characteristic would need to be combined with optical response characteristics of other sample components to obtain a combined optical response characteristic of the sample as a whole.
  • the other components' response characteristics might be similarly obtained from their own interpolation models, or might be obtained directly from theory in real time. (For example, a non-diffractive layer's optical response characteristic can be computed from theory very easily and quickly.)
  • polarizing properties of the instrument's illumination and collection optics may be separately represented by Jones matrices (or alternatively, Mueller matrices), which would be combined with the sample's response characteristic to calculate a Jones (or Mueller) matrix of the entire optical system (illumination optics, sample, and collection optics). If the polarization or other characteristics of the instrument are varied as the measurement signal is acquired, this calculation may be repeated for each of a number of instrument configurations.
  • an ellisometer typically has a polarization-modulating element, and its measured signal characteristic is typically a composition of signals associated with various states of the modulating element.
  • the optical system's response characteristic is used to calculate the predicted signal characteristic by effectively simulating the electromagnetic field intensity on the optical sensor elements.
  • Each sensor element may respond to radiation comprising a range of wavelengths or corresponding to a range of incidence or collection directions at the sample, so this calculation may comprise a summation over wavelengths or directions.
  • the directional summation may represent a coherent, incoherent, or partially coherent superposition of optical response components corresponding to different incidence or collection directions.
  • the instrument-related data that enters into the predicted signal calculation may include factors such as optical calibrations and the illumination source intensity, which vary between instruments and with time. But rather than incorporating all of these factors in the predicted signal characteristic, at least some of these factors are more typically applied in an inverse manner to the sensor signal data to obtain a measured signal characteristic such as an "effective" reflectivity or Stokes vector that has minimal instrument dependence and is primarily a function of only the sample.
  • the signal characteristic comprises reflectivity data or ellipsometric quantities such as tan ⁇ and cos ⁇ (Refs 12, 16), which characterize the sample independently of the instrument.
  • tan ⁇ and cos ⁇ reflectivity data or ellipsometric quantities
  • cos ⁇ cos ⁇
  • “Mueller matrix” components are suitable signal characteristics, from this perspective.
  • the Mueller matrix for a conventional rotating-polarizer ellipsometer contains two independent, dimensionless factors, cos(2 ⁇ ) and sin(2 ⁇ )cos( ⁇ ) , which have a linear dependence on the sensor signals.
  • a signal characteristic such as "effective reflectivity" (e.g. R in Eq.
  • the "effective" quantity is a summation or average over reflecting zones, or over wavelengths or incidence directions.
  • the predicted and measured optical signal response characteristics are compared, and the comparison fit error is typically quantified in terms of a "fit metric" such as a chi-square metric ( ⁇ 2 ), which is defined as
  • y denotes a measurable signal characteristic comprising multiple signal components y .
  • x denotes a set of measurement parameters (e.g., film thicknesses, linewidth, etc.);
  • y pred (x) denotes the predicted signal for ;
  • yTM eas represents the measured signal characteristic;
  • wt j is a non-negative weighting factor.
  • the definition of y TM eas may incorporate factors such as the instrument's optical calibrations and the illumination source intensity, as well as the sensor signal data.
  • yf p ed (x) may also include such instrument- related factors, as well as the sample parameter dependence.
  • the algorithm designer has some degree of freedom in allocating the instrument-related factors between y eas and y pred (x) (e.g., by applying a common additive shift or dividing a common factor out of both terms).
  • the ⁇ 2 metric has the property that is is always non-negative, and is zero if and only if there is a perfect match between yf p ed (x) and yTM"" for all j .
  • the objective of a fitting optimization algorithm based on the ⁇ 2 metric is to find a measured parameter set x that minimizes ⁇ 2 . If wt j is set to 1 in Eq. 24, ⁇ 2 is similar to the fit metric employed by MMSE algorithms; however measurement precision can be optimized by defining wt j to be the reciprocal variance of yTM eas ,
  • ⁇ 2 (y pred (x) - y meas ) ⁇ (coy y pred ( , x) + coy y meas y 1 (y pred (x) - y meas )
  • y pred (x) and y meas are column matrices comprising the y pred (x) and y e s elements; cov y pred (p) and covy me s are associated covariance matrices; and the "T" superscript indicates matrix transposition.
  • the fitting optimization algorithm iteratively adjusts x to minimize ⁇ 2 .
  • x is a "trial measurement parameter set” (i.e. an ordered set of numeric values, one for each measurement parameter), x includes the "trial inte ⁇ olation parameter set", the elements of which correspond to inte ⁇ olation parameters, (x may also include other sample parameters that are not associated with the invention's subject diffractive structure.)
  • the minimization method includes two stages, a preliminary "grid search", and subsequent “refinement”. In the first stage, a multi-dimensional grid of trial measurement parameter sets is defined, and ⁇ 2 is calculated for every point x on the grid. (In this context "grid point” is synonymous with "trial measurement parameter set”.
  • the grid points may, in some embodiments, correspond to the database inte ⁇ olation points.
  • One or more trial parameter sets are selected from the grid for subsequent refinement.
  • Fig. 8 conceptually illustrates the selection process.
  • the grid search scans the grid points for parameter sets that could potentially be close to a global minimum of ⁇ 2 over a parameter domain that includes the grid points. It is not sufficient to just select the grid point with the lowest ⁇ 2 because, as illustrated in Fig. 8, this strategy could yield false results due to the grid's limited sampling density.
  • the curve 801 illustrates ⁇ 2 as a function of a scalar parameter value, .
  • Grid points (e.g. point 802) are represented as squares on curve 801. The lowest ⁇ 2 on the grid is at point 802; but the true minimum (and the correct x value) is located at point 803, which is between grid points 804 and 805.
  • the grid search does not miss the global ⁇ 2 minimum, it first finds all local minima on the grid.
  • the grid local minima are points 802, 805, and 806.
  • the local minima search will typically find a large number of points, such as point 806, which have very poor fits and are obviously not near the correct solution.
  • the bad points are filtered out by applying a ⁇ 2 threshold criterion. But again, due to the database's limited sampling density, it is not sufficient to just exclude all points above the ⁇ 2 threshold. For example, if this strategy were applied, the threshold level 807 in Fig. 8 would exclude the grid point 805 nearest the global minimum 803, but would accept the false minimum 802.
  • the grid search strategy illustrated in Fig. 8 generalizes in a straightforward manner to the more general case where there are multiple measurement parameter values and x is a vector-valued entity spanning a multi-dimensional parameter search range.
  • ⁇ 2 is sampled on a multi-dimensional grid. Local minima are identified, and an uncertainty range for each minimum is determined, based on comparisons of each point's ⁇ 2 value with those of adjacent points (including diagonal adjacencies); and points whose uncertainty ranges extend at least partially below the ⁇ 2 threshold are selected for further refinement.
  • Each selected grid point is used as a "seed" for subsequent refinement.
  • the refinement is performed by an automated minimization algorithm that adjusts x to minimize ⁇ 2 .
  • x is not limited to discrete points represented in the grid or in the inte ⁇ olation database; it can be varied continuously within a defined parameter domain.
  • the minimization algorithm iterates from the seed value until a defined termination criterion is satisfied (e.g., until incremental changes in x , or in ⁇ 2 , fall below a certain threshold).
  • Suitable minimization algorithms include as MATLAB's "lsqnonlin” routine or the EVISL "BCLSF/DBCLSF” or "BCLSJ/DBCLSJ” routines.
  • the runtime performance can be further enhanced by providing the minimizer the first-order derivatives of ⁇ ; with respect to the x components (measurement parameters), along with S j itself.
  • a useful feature of the database inte ⁇ olation method is that these derivatives can be easily computed, and the fitting optimization algorithm should preferably make use of the derivatives.
  • the refinement stage may be divided into several sub-stages using progressively more accurate (though more time-consuming) calculation models. For example, the refinement might be done first using a linear inte ⁇ olation model for the optical response characteristic, and then (after initial termination criteria of the minimization algorithm have been met), the refinement may be continued using cubic inte ⁇ olation. Also, some measurement parameters, such as material-related parameters, might be initially held fixed when the refinement is initiated, and then allowed to vary as the refinement approaches convergence.

Landscapes

  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • General Health & Medical Sciences (AREA)
  • Immunology (AREA)
  • Life Sciences & Earth Sciences (AREA)
  • Chemical & Material Sciences (AREA)
  • Analytical Chemistry (AREA)
  • Biochemistry (AREA)
  • Pathology (AREA)
  • Health & Medical Sciences (AREA)
  • Optics & Photonics (AREA)
  • Investigating Or Analysing Materials By Optical Means (AREA)
  • Length Measuring Devices By Optical Means (AREA)
  • Testing Of Optical Devices Or Fibers (AREA)
  • Holo Graphy (AREA)
  • Testing Or Measuring Of Semiconductors Or The Like (AREA)
  • Complex Calculations (AREA)

Abstract

Un procédé d'interpolation de bases de données est utilisé pour calculer rapidement une caractéristique prévue de la réponse optique d'une microstructure à diffraction (501) se présentant comme une partie du processus de mesure optique en temps réel. La réponse optique interpolée (602) est une fonction continue et (dans un mode de réalisation préféré) (801) lisse des paramètres de mesure (X); elle est appariée à la réponse optique calculée théoriquement aux points d'interpolation stockés dans la base de données (701, 702).
EP01957510A 2000-08-10 2001-08-09 Procede d'interpolation de bases de donnees destine a la mesure optique de microstructures a diffraction Withdrawn EP1309849A2 (fr)

Applications Claiming Priority (5)

Application Number Priority Date Filing Date Title
US22445100P 2000-08-10 2000-08-10
US224451P 2000-08-10
US27095601P 2001-02-22 2001-02-22
US270956P 2001-02-22
PCT/US2001/024940 WO2002014840A2 (fr) 2000-08-10 2001-08-09 Procede d'interpolation de bases de donnees destine a la mesure optique de microstructures a diffraction

Publications (1)

Publication Number Publication Date
EP1309849A2 true EP1309849A2 (fr) 2003-05-14

Family

ID=26918728

Family Applications (1)

Application Number Title Priority Date Filing Date
EP01957510A Withdrawn EP1309849A2 (fr) 2000-08-10 2001-08-09 Procede d'interpolation de bases de donnees destine a la mesure optique de microstructures a diffraction

Country Status (5)

Country Link
US (3) US6768967B2 (fr)
EP (1) EP1309849A2 (fr)
JP (1) JP2004507719A (fr)
AU (1) AU2001279247A1 (fr)
WO (1) WO2002014840A2 (fr)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US11525993B2 (en) 2018-06-29 2022-12-13 Illumina, Inc. Predicting structured illumination parameters

Families Citing this family (111)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6728663B2 (en) 2000-09-13 2004-04-27 Accent Optical Technologies, Inc. Structure identification using scattering signatures
US7115858B1 (en) 2000-09-25 2006-10-03 Nanometrics Incorporated Apparatus and method for the measurement of diffracting structures
US7099005B1 (en) * 2000-09-27 2006-08-29 Kla-Tencor Technologies Corporation System for scatterometric measurements and applications
US6900892B2 (en) * 2000-12-19 2005-05-31 Kla-Tencor Technologies Corporation Parametric profiling using optical spectroscopic systems
JP2004529330A (ja) 2001-03-02 2004-09-24 アクセント オプティカル テクノロジーズ，インク． スキャタロメトリを使用するライン・プロファイルの非対称測定
JP3647378B2 (ja) * 2001-03-02 2005-05-11 キヤノン株式会社 マルチプローブを用いた形状測定装置及び測定方法
US7515279B2 (en) 2001-03-02 2009-04-07 Nanometrics Incorporated Line profile asymmetry measurement
US6898537B1 (en) 2001-04-27 2005-05-24 Nanometrics Incorporated Measurement of diffracting structures using one-half of the non-zero diffracted orders
US6713753B1 (en) 2001-07-03 2004-03-30 Nanometrics Incorporated Combination of normal and oblique incidence polarimetry for the characterization of gratings
US6785638B2 (en) * 2001-08-06 2004-08-31 Timbre Technologies, Inc. Method and system of dynamic learning through a regression-based library generation process
US6867866B1 (en) * 2001-08-10 2005-03-15 Therma-Wave, Inc. CD metrology analysis using green's function
US6678046B2 (en) * 2001-08-28 2004-01-13 Therma-Wave, Inc. Detector configurations for optical metrology
US7061615B1 (en) 2001-09-20 2006-06-13 Nanometrics Incorporated Spectroscopically measured overlay target
WO2003032085A2 (fr) * 2001-10-10 2003-04-17 Accent Optical Technologies, Inc. Determination du centre d'un point focal par analyse croisee
US6898596B2 (en) * 2001-10-23 2005-05-24 Therma-Wave, Inc. Evolution of library data sets
US7028016B2 (en) * 2001-11-16 2006-04-11 Sun Microsystems, Inc Applying term consistency to the solution of unconstrained interval global optimization problems
JP4938219B2 (ja) * 2001-12-19 2012-05-23 ケーエルエー−テンカー コーポレイション 光学分光システムを使用するパラメトリック・プロフィーリング
US6609086B1 (en) * 2002-02-12 2003-08-19 Timbre Technologies, Inc. Profile refinement for integrated circuit metrology
US7247345B2 (en) * 2002-03-25 2007-07-24 Ulvac, Inc. Optical film thickness controlling method and apparatus, dielectric multilayer film and manufacturing apparatus thereof
US6949462B1 (en) 2002-04-04 2005-09-27 Nanometrics Incorporated Measuring an alignment target with multiple polarization states
US6982793B1 (en) 2002-04-04 2006-01-03 Nanometrics Incorporated Method and apparatus for using an alignment target with designed in offset
TWI273217B (en) * 2002-04-17 2007-02-11 Accent Optical Tech Inc Scatterometric measurement of undercut multi-layer diffracting structures
US6947135B2 (en) * 2002-07-01 2005-09-20 Therma-Wave, Inc. Reduced multicubic database interpolation method for optical measurement of diffractive microstructures
US20040125453A1 (en) * 2002-07-03 2004-07-01 Mcaulay Alastair D. Inverse computation of phase masks for two layer diffractive optic element system
US6919964B2 (en) * 2002-07-09 2005-07-19 Therma-Wave, Inc. CD metrology analysis using a finite difference method
US7321433B2 (en) 2002-07-12 2008-01-22 Dansk Fundamental Metrologi A/S Method and apparatus for optically measuring the topography of nearly planar periodic structures
US6992764B1 (en) 2002-09-30 2006-01-31 Nanometrics Incorporated Measuring an alignment target with a single polarization state
US6950190B2 (en) * 2003-01-09 2005-09-27 Therma-Wave, Inc. Scatterometry for junction metrology
US20080246951A1 (en) * 2007-04-09 2008-10-09 Phillip Walsh Method and system for using reflectometry below deep ultra-violet (DUV) wavelengths for measuring properties of diffracting or scattering structures on substrate work-pieces
US8564780B2 (en) 2003-01-16 2013-10-22 Jordan Valley Semiconductors Ltd. Method and system for using reflectometry below deep ultra-violet (DUV) wavelengths for measuring properties of diffracting or scattering structures on substrate work pieces
DE10302868B4 (de) * 2003-01-25 2008-07-03 Fraunhofer-Gesellschaft zur Förderung der angewandten Forschung e.V. Verfahren zur Bestimmung von Strukturparametern einer Oberfläche mit einem lernfähigen System
US7069153B2 (en) * 2003-01-28 2006-06-27 Therma-Wave, Inc. CD metrology method
US7233390B2 (en) * 2003-03-31 2007-06-19 Therma-Wave, Inc. Scatterometry for samples with non-uniform edges
US7119893B2 (en) * 2003-04-10 2006-10-10 Accent Optical Technologies, Inc. Determination of center of focus by parameter variability analysis
JP4134806B2 (ja) * 2003-04-25 2008-08-20 ブラザー工業株式会社 色変換装置、画像形成装置および色変換プログラム
US7085676B2 (en) * 2003-06-27 2006-08-01 Tokyo Electron Limited Feed forward critical dimension control
DE102004034398B4 (de) * 2004-07-16 2009-12-03 Universität Potsdam Verfahren zum Ermitteln einer linearen Beziehung aus elektronisch speicherbaren Meßdaten
US20060117293A1 (en) * 2004-11-30 2006-06-01 Nigel Smith Method for designing an overlay mark
TWI269870B (en) 2004-12-30 2007-01-01 Ind Tech Res Inst Method for deciding structure parameters of a grating
US7478019B2 (en) * 2005-01-26 2009-01-13 Kla-Tencor Corporation Multiple tool and structure analysis
US7764377B2 (en) 2005-08-22 2010-07-27 Applied Materials, Inc. Spectrum based endpointing for chemical mechanical polishing
US7409260B2 (en) * 2005-08-22 2008-08-05 Applied Materials, Inc. Substrate thickness measuring during polishing
US7406394B2 (en) * 2005-08-22 2008-07-29 Applied Materials, Inc. Spectra based endpointing for chemical mechanical polishing
US8392012B2 (en) 2008-10-27 2013-03-05 Applied Materials, Inc. Multiple libraries for spectrographic monitoring of zones of a substrate during processing
US8260446B2 (en) 2005-08-22 2012-09-04 Applied Materials, Inc. Spectrographic monitoring of a substrate during processing using index values
DE102005045362B4 (de) * 2005-09-22 2012-03-22 Siemens Ag Vorrichtung zur Positionsbestimmung eines medizinischen Instruments, dazugehörige bildgebende Untersuchungseinrichtung nebst dazugehörigem Verfahren
US7423465B2 (en) * 2006-01-27 2008-09-09 Micron Technology, Inc. Duty cycle error calculation circuit for a clock generator having a delay locked loop and duty cycle correction circuit
US7567351B2 (en) * 2006-02-02 2009-07-28 Kla-Tencor Corporation High resolution monitoring of CD variations
DE102006017283A1 (de) * 2006-04-12 2007-10-18 Infineon Technologies Ag Verfahren und Messvorrichtung zur ellipsometrischen Vermessung von Strukturelementen und Verwendung der Messvorrichtung
US8294907B2 (en) 2006-10-13 2012-10-23 Asml Netherlands B.V. Inspection method and apparatus, lithographic apparatus, lithographic processing cell and device manufacturing method
US7998358B2 (en) 2006-10-31 2011-08-16 Applied Materials, Inc. Peak-based endpointing for chemical mechanical polishing
US7710572B2 (en) * 2006-11-30 2010-05-04 Asml Netherlands B.V. Inspection method and apparatus, lithographic apparatus, lithographic processing cell and device manufacturing method
US20080129986A1 (en) * 2006-11-30 2008-06-05 Phillip Walsh Method and apparatus for optically measuring periodic structures using orthogonal azimuthal sample orientations
US7444198B2 (en) * 2006-12-15 2008-10-28 Applied Materials, Inc. Determining physical property of substrate
KR101643992B1 (ko) 2007-02-23 2016-07-29 어플라이드 머티어리얼스, 인코포레이티드 연마 엔드포인트들을 결정하기 위한 스펙트럼 사용
US7840375B2 (en) * 2007-04-02 2010-11-23 Applied Materials, Inc. Methods and apparatus for generating a library of spectra
JP5270109B2 (ja) * 2007-05-23 2013-08-21 ルネサスエレクトロニクス株式会社 半導体集積回路装置の製造方法
US7460237B1 (en) * 2007-08-02 2008-12-02 Asml Netherlands B.V. Inspection method and apparatus, lithographic apparatus, lithographic processing cell and device manufacturing method
US20090182529A1 (en) * 2008-01-14 2009-07-16 International Business Machines Corporation Determining signal quality of optical metrology tool
US7869044B2 (en) * 2008-01-16 2011-01-11 Optotrace Technologies, Inc. Optical sensing system based on a micro-array structure
US8300980B2 (en) * 2008-03-18 2012-10-30 Sony Corporation System, method and computer program product for providing a high resolution texture within an image
US20090275265A1 (en) * 2008-05-02 2009-11-05 Applied Materials, Inc. Endpoint detection in chemical mechanical polishing using multiple spectra
EP2120143B1 (fr) * 2008-05-13 2011-08-31 dspace digital signal processing and control engineering GmbH Procédé d'exécution de tâches destinée au calcul d'un signal devant être simulé en temps réel
ATE518171T1 (de) * 2008-05-29 2011-08-15 Dspace Gmbh Verfahren und simulator zur echtzeitberechnung der zustandsgrössen eines prozessmodells
US20100103422A1 (en) * 2008-10-27 2010-04-29 Applied Materials, Inc. Goodness of fit in spectrographic monitoring of a substrate during processing
US8352061B2 (en) 2008-11-14 2013-01-08 Applied Materials, Inc. Semi-quantitative thickness determination
DE102009033421A1 (de) * 2009-07-16 2011-01-20 Christian-Albrechts-Universität Zu Kiel Verfahren und Anordnung zum Rekonstruieren der Quelle eines elektromagnetischen Feldes
US8525993B2 (en) * 2009-10-07 2013-09-03 Nanometrics Incorporated Scatterometry measurement of asymmetric structures
JP5968783B2 (ja) * 2009-11-03 2016-08-10 アプライド マテリアルズ インコーポレイテッドＡｐｐｌｉｅｄ Ｍａｔｅｒｉａｌｓ，Ｉｎｃｏｒｐｏｒａｔｅｄ スペクトルの等高線図のピーク位置と時間の関係を使用する終点方法
US20110143115A1 (en) * 2009-12-10 2011-06-16 Xerox Corporation Intermediate transfer member and method of manufacture
US20110188901A1 (en) * 2009-12-10 2011-08-04 Xerox Corporation Intermediate transfer member and method of manufacture
US7993735B1 (en) 2010-04-13 2011-08-09 Xerox Corporation Intermediate transfer member and method of manufacture
US8954186B2 (en) 2010-07-30 2015-02-10 Applied Materials, Inc. Selecting reference libraries for monitoring of multiple zones on a substrate
US9606453B2 (en) 2010-09-30 2017-03-28 Kla-Tencor Corporation Method and system for providing tool induced shift using a sub-sampling scheme
US8867041B2 (en) 2011-01-18 2014-10-21 Jordan Valley Semiconductor Ltd Optical vacuum ultra-violet wavelength nanoimprint metrology
KR101794537B1 (ko) * 2011-01-21 2017-11-07 삼성전자주식회사 데이터 처리 장치 및 방법
US8565379B2 (en) 2011-03-14 2013-10-22 Jordan Valley Semiconductors Ltd. Combining X-ray and VUV analysis of thin film layers
US9075566B2 (en) 2012-03-02 2015-07-07 Microsoft Technoogy Licensing, LLC Flexible hinge spine
US9134807B2 (en) 2012-03-02 2015-09-15 Microsoft Technology Licensing, Llc Pressure sensitive key normalization
US10255385B2 (en) * 2012-03-28 2019-04-09 Kla-Tencor Corporation Model optimization approach based on spectral sensitivity
US20130300590A1 (en) 2012-05-14 2013-11-14 Paul Henry Dietz Audio Feedback
CN102798342B (zh) * 2012-08-02 2014-11-12 华中科技大学 一种用于光学散射测量的基于拟合误差插值的库匹配方法
EP2959262A4 (fr) * 2013-02-21 2016-09-28 Nova Measuring Instr Ltd Procédé et système de mesure de phase optique
US10386729B2 (en) 2013-06-03 2019-08-20 Kla-Tencor Corporation Dynamic removal of correlation of highly correlated parameters for optical metrology
JP6273705B2 (ja) * 2013-07-18 2018-02-07 セイコーエプソン株式会社 検量線作成方法および検量線作成装置
US9465144B2 (en) * 2013-12-30 2016-10-11 Raytheon Company Hybrid grin diffractive optics
CN105444666B (zh) * 2014-05-29 2018-05-25 睿励科学仪器（上海）有限公司 用于光学关键尺寸测量的方法及装置
US9304235B2 (en) 2014-07-30 2016-04-05 Microsoft Technology Licensing, Llc Microfabrication
US10324733B2 (en) 2014-07-30 2019-06-18 Microsoft Technology Licensing, Llc Shutdown notifications
US9787576B2 (en) 2014-07-31 2017-10-10 Microsoft Technology Licensing, Llc Propagating routing awareness for autonomous networks
US10592080B2 (en) 2014-07-31 2020-03-17 Microsoft Technology Licensing, Llc Assisted presentation of application windows
US10678412B2 (en) 2014-07-31 2020-06-09 Microsoft Technology Licensing, Llc Dynamic joint dividers for application windows
US10254942B2 (en) 2014-07-31 2019-04-09 Microsoft Technology Licensing, Llc Adaptive sizing and positioning of application windows
US9535253B2 (en) 2015-02-09 2017-01-03 Microsoft Technology Licensing, Llc Display system
US9372347B1 (en) 2015-02-09 2016-06-21 Microsoft Technology Licensing, Llc Display system
US9423360B1 (en) 2015-02-09 2016-08-23 Microsoft Technology Licensing, Llc Optical components
US9429692B1 (en) 2015-02-09 2016-08-30 Microsoft Technology Licensing, Llc Optical components
US10317677B2 (en) 2015-02-09 2019-06-11 Microsoft Technology Licensing, Llc Display system
US10018844B2 (en) 2015-02-09 2018-07-10 Microsoft Technology Licensing, Llc Wearable image display system
US9827209B2 (en) 2015-02-09 2017-11-28 Microsoft Technology Licensing, Llc Display system
US9513480B2 (en) 2015-02-09 2016-12-06 Microsoft Technology Licensing, Llc Waveguide
US11086216B2 (en) 2015-02-09 2021-08-10 Microsoft Technology Licensing, Llc Generating electronic components
US11313809B1 (en) * 2016-05-04 2022-04-26 Kla-Tencor Corporation Process control metrology
GB201615745D0 (en) 2016-09-15 2016-11-02 Gb Gas Holdings Ltd System for analysing data relationships to support query execution
EP3480659A1 (fr) * 2017-11-01 2019-05-08 ASML Netherlands B.V. Estimation de données en métrologie
JP7129356B2 (ja) * 2019-02-13 2022-09-01 キオクシア株式会社 測定方法
CN111879236B (zh) * 2020-07-14 2021-09-24 上海精测半导体技术有限公司 自理论光谱库确定待测样品参数的方法及测量设备
CN113591290B (zh) * 2021-07-20 2024-02-06 上海华虹宏力半导体制造有限公司 Opc模型仿真方法
CN113566739B (zh) * 2021-08-23 2023-06-13 上海精测半导体技术有限公司 一种用于光学散射的库匹配方法、系统、服务器及存储介质
CN114322836B (zh) * 2022-03-17 2022-05-27 板石智能科技(深圳)有限公司 基于启发式搜索的周期纳米结构形貌参数测量方法及装置
IL293633B1 (en) * 2022-06-06 2024-02-01 Nova Ltd A system and method for building a library and using it in measurements on designed buildings

Family Cites Families (43)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US33945A (en) * 1861-12-17 Improvement in lamps
US192847A (en) * 1877-07-10 Improvement in padlocks
US5957A (en) * 1848-12-05 Improvement in copying surfaces by electricity
DE3274759D1 (en) * 1981-08-04 1987-01-29 Oesterr Forsch Seibersdorf Method of measuring the coating thickness of clad wires or pipes
US4555767A (en) * 1982-05-27 1985-11-26 International Business Machines Corporation Method and apparatus for measuring thickness of epitaxial layer by infrared reflectance
US4689754A (en) * 1985-02-21 1987-08-25 The Perkin-Elmer Corporation Optimization apparatus and procedure
GB8601176D0 (en) * 1986-01-17 1986-02-19 Infrared Eng Ltd Sensing
FR2598797B1 (fr) * 1986-05-07 1990-05-11 Nippon Telegraph & Telephone Procede de mesure et/ou d'ajustement du deplacement d'un objet et appareil pour la mise en oeuvre de ce procede
US4994990A (en) * 1987-02-03 1991-02-19 Citizen Watch Co., Ltd. Micro-dimensional measurement apparatus
US4757207A (en) 1987-03-03 1988-07-12 International Business Machines Corporation Measurement of registration of overlaid test patterns by the use of reflected light
DE3801027A1 (de) * 1988-01-15 1989-07-27 Saunalux Gmbh Products & Co Kg Verfahren und geraet zur grossflaechigen bestrahlung des menschlichen koerpers
JPH0731050B2 (ja) * 1988-12-29 1995-04-10 オリンパス光学工業株式会社 光学式膜厚測定装置
GB2242976A (en) * 1990-04-12 1991-10-16 Rank Taylor Hobson Ltd Measuring surface characteristics
US5315513A (en) * 1991-10-29 1994-05-24 The United States Of America As Represented By The Secretary Of The Air Force System for modelling moderate resolution atmospheric propagation
US5262635A (en) * 1991-11-20 1993-11-16 Bio-Rad Laboratories, Inc. Techniques for correcting non-linearity in a photodetector using predefined calibration information
EP0961475B1 (fr) * 1992-05-15 2004-10-13 Toyota Jidosha Kabushiki Kaisha Balayeur multispectral d'image
JPH074922A (ja) * 1993-06-21 1995-01-10 Jasco Corp 半導体多層薄膜膜厚測定装置およびその測定方法
US5428558A (en) * 1993-12-17 1995-06-27 The Perkin-Elmer Corporation Correction of spectra for stray radiation
KR0133637B1 (ko) * 1994-06-21 1998-04-23 정명세 새로운 내삽공식을 이용하여 복사온도계를 교정하는 방법
US5607800A (en) 1995-02-15 1997-03-04 Lucent Technologies Inc. Method and arrangement for characterizing micro-size patterns
US5905822A (en) * 1995-07-13 1999-05-18 Fuji Photo Film Co., Ltd. Interpolating operation method and apparatus for image signals
US6008906A (en) * 1995-08-25 1999-12-28 Brown University Research Foundation Optical method for the characterization of the electrical properties of semiconductors and insulating films
US5844684A (en) * 1997-02-28 1998-12-01 Brown University Research Foundation Optical method for determining the mechanical properties of a material
US6037614A (en) * 1997-03-07 2000-03-14 California Institute Of Technology Methods for manufacturing group IV element alloy semiconductor materials and devices that include such materials
US5867276A (en) 1997-03-07 1999-02-02 Bio-Rad Laboratories, Inc. Method for broad wavelength scatterometry
US5993386A (en) * 1997-07-15 1999-11-30 Ericsson; Arthur Dale Computer assisted method for the diagnosis and treatment of illness
US6057171A (en) * 1997-09-25 2000-05-02 Frequency Technology, Inc. Methods for determining on-chip interconnect process parameters
US5963329A (en) * 1997-10-31 1999-10-05 International Business Machines Corporation Method and apparatus for measuring the profile of small repeating lines
US6483580B1 (en) 1998-03-06 2002-11-19 Kla-Tencor Technologies Corporation Spectroscopic scatterometer system
IL123727A (en) * 1998-03-18 2002-05-23 Nova Measuring Instr Ltd Method and apparatus for measurement of patterned structures
US6476920B1 (en) * 1998-03-18 2002-11-05 Nova Measuring Instruments, Ltd. Method and apparatus for measurements of patterned structures
US6780657B2 (en) * 1998-03-19 2004-08-24 Kabushiki Kaisha Toshiba Temperature measuring method and apparatus, measuring method for the thickness of the formed film, measuring apparatus for the thickness of the formed film thermometer for wafers
US6541287B2 (en) * 1998-03-19 2003-04-01 Kabushiki Kaisha Toshiba Temperature measuring method and apparatus, measuring method for the thickness of the formed film, measuring apparatus for the thickness of the formed film thermometer for wafers
US6242739B1 (en) * 1998-04-21 2001-06-05 Alexander P. Cherkassky Method and apparatus for non-destructive determination of film thickness and dopant concentration using fourier transform infrared spectrometry
US6049220A (en) * 1998-06-10 2000-04-11 Boxer Cross Incorporated Apparatus and method for evaluating a wafer of semiconductor material
US5884684A (en) * 1998-07-16 1999-03-23 Jefferson; Samuel Alexander Telescopic sun screen assembly
AU3187100A (en) * 1999-03-10 2000-09-28 Nova Measuring Instruments Ltd. Method and apparatus for monitoring a chemical mechanical planarization process applied to metal-based patterned objects
US6542829B1 (en) * 1999-09-22 2003-04-01 Coventor, Inc. Characterization of microelectromechanical structures
US6485872B1 (en) * 1999-12-03 2002-11-26 Mks Instruments, Inc. Method and apparatus for measuring the composition and other properties of thin films utilizing infrared radiation
US6340602B1 (en) * 1999-12-10 2002-01-22 Sensys Instruments Method of measuring meso-scale structures on wafers
US6819426B2 (en) * 2001-02-12 2004-11-16 Therma-Wave, Inc. Overlay alignment metrology using diffraction gratings
US6947135B2 (en) * 2002-07-01 2005-09-20 Therma-Wave, Inc. Reduced multicubic database interpolation method for optical measurement of diffractive microstructures
US7069153B2 (en) * 2003-01-28 2006-06-27 Therma-Wave, Inc. CD metrology method

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
None *
See also references of WO0214840A3 *

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US11525993B2 (en) 2018-06-29 2022-12-13 Illumina, Inc. Predicting structured illumination parameters

Also Published As

Publication number Publication date
US20050280832A1 (en) 2005-12-22
AU2001279247A1 (en) 2002-02-25
US6768967B2 (en) 2004-07-27
US20020038196A1 (en) 2002-03-28
JP2004507719A (ja) 2004-03-11
WO2002014840A2 (fr) 2002-02-21
US7069182B2 (en) 2006-06-27
US6950780B2 (en) 2005-09-27
US20040167722A1 (en) 2004-08-26
WO2002014840A3 (fr) 2002-08-15

Similar Documents

Publication Publication Date Title
US6768967B2 (en) Database interpolation method for optical measurement of diffractive microstructures
US7280230B2 (en) Parametric profiling using optical spectroscopic systems
US7099005B1 (en) System for scatterometric measurements and applications
US7069153B2 (en) CD metrology method
US7061627B2 (en) Optical scatterometry of asymmetric lines and structures
US8139232B2 (en) Multiple measurement techniques including focused beam scatterometry for characterization of samples
US6900892B2 (en) Parametric profiling using optical spectroscopic systems
KR101342410B1 (ko) 주기적인 회절 구조를 포함하는 층을 갖는 샘플을 측정하는시스템
US10502692B2 (en) Automated metrology system selection
IL268861A (en) The robust coverage metrology process is based on optical spectrometry
TW201727250A (zh) 使用影像之以模型為基礎之度量
Germer et al. Developing an uncertainty analysis for optical scatterometry
KR20140135732A (ko) 광 임계 치수(ocd) 계측을 위한 레일리 파장의 개구수 적분
US7602509B1 (en) Method for selecting optical configuration for high-precision scatterometric measurement
TWI447603B (zh) 使用壓縮傅立葉空間來模擬二維週期圖案
Mills et al. Spectral ellipsometry on patterned wafers
Endres et al. Numerical investigations of the influence of different commonly applied approximations in scatterometry
US7202958B1 (en) Modeling a sample with an underlying complicated structure
Lee et al. Optical system to extract reflection coefficients and optical admittances of a thin film stack and its application in coating monitoring
박지훈 Region Classification and Thin-film Thickness Measurement Using Color Camera Imaging Mueller Matrix Ellipsometry
CA2086848A1 (fr) Procede et appareil de representation des variations d'epaisseur a resolution spatiale

Legal Events

Date Code Title Description
PUAI Public reference made under article 153(3) epc to a published international application that has entered the european phase

Free format text: ORIGINAL CODE: 0009012

17P Request for examination filed

Effective date: 20030307

AK Designated contracting states

Designated state(s): AT BE CH CY DE DK ES FI FR GB GR IE IT LI LU MC NL PT SE TR

AX Request for extension of the european patent

Extension state: AL LT LV MK RO SI

RBV Designated contracting states (corrected)

Designated state(s): DE FR GB NL

GRAP Despatch of communication of intention to grant a patent

Free format text: ORIGINAL CODE: EPIDOSNIGR1

STAA Information on the status of an ep patent application or granted ep patent

Free format text: STATUS: THE APPLICATION IS DEEMED TO BE WITHDRAWN

18D Application deemed to be withdrawn

Effective date: 20070717